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On a Result of A. M. Macbeath on Normal Subgroups of a Fuchsian Group

Published online by Cambridge University Press:  20 November 2018

W. Jonsson
W. Jonsson*
Affiliation:
McGill University, Montreal, Quebec
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A. M. Macbeath, in November 1965, communicated the following theorem to me which he proved with the aid of the Lefschetz fixed point formula.

Theorem. If Γ is a Fuchsian group and N a torsion free normal subgroup, then the rank of N/[Γ, N] is twice the genus of the orbit space D/Γ where D denotes the hyperbolic plane which Γ acts.

This theorem will follow from a consideration of the exact sequence

*

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 13 , Issue 1 , March 1970 , pp. 15 - 16
Copyright
Copyright © Canadian Mathematical Society 1970

References

1. Cartan, H., and Eilenberg, S., Homological Algebra, Princeton, 1956.Google Scholar
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3. Stammbach, U., Anwendung der homologietheorie auf zentralreihen und invarianten von pr?sentierungen, Math. Z. 94 (1966), 157-177.Google Scholar
4. Sah, C. H., Groups related to compact Rieman surfaces, Acta Math. 123 (1969), 13-42.Google Scholar